A) \[x=10.25\sin \,(\omega \,t+\phi )\]
B) \[x=10.25\sin \,(\omega \,t-\phi )\]
C) \[x=11.25\sin \,(\omega \,t+\phi )\]
D) \[x=11.25\sin \,(\omega \,t-\phi )\]
Correct Answer: C
Solution :
The resultant equation is \[x=A\sin (\omega \,t+\phi )\] \[\Sigma {{A}_{x}}=2+4\cos {{30}^{o}}+6\cos {{60}^{o}}=8.46\] and \[\Sigma {{A}_{y}}=4\sin {{30}^{o}}+6\cos {{30}^{o}}=7.2\] \[\therefore \] \[A=\sqrt{{{(\Sigma {{A}_{x}})}^{2}}+{{(\Sigma {{A}_{y}})}^{2}}}\] \[=\sqrt{{{(8.46)}^{2}}+{{(7.2)}^{2}}}=11.25\] and \[\tan \phi \frac{\Sigma {{A}_{y}}}{\Sigma {{A}_{y}}}=\frac{7.2}{8.46}=0.85\] \[\Rightarrow \] \[\phi ={{\tan }^{-1}}(0.85)={{40.4}^{o}}\] Thus, the displacement equation of combined motion is \[x=11.25\sin \,\,(\omega \,t+\phi )\] where, \[\phi ={{40.4}^{o}}\]You need to login to perform this action.
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